Relativistic Hydrodynamics is an effective theory; it
has been proved to be reasonably successful in describing
various systems' collective (long wavelength) behavior
ranging from relativistic heavy-ion collision to condensed matter system. Relativistic hydrodynamical theory can be expressed as the gradient expansion of the hydrodynamic variable around the local equilibrium state. The theory with zeroth-order gradients is called ideal hydrodynamics, and with first-order gradients is called first-order hydrodynamics, and so on. Relativistic Navier-Stokes equations show superluminal signal propagation as well as instability [1]}, [2]}. The second-order hydrodynamic theory is introduced to resolve the stability and causality problem of NS equations [3]}, [4]}. Recently, the solution to the stability and causality of first-order hydrodynamics have proposed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK) theory [5]}, [6]}, [7]} by introducing a general hydrodynamic frame.
